In the paper and plastic film industries, a dancer roll is widely used as a buffer between first and second sets of driving rolls, or first and second nips, which drive a continuous web. The dancer roll, which is positioned between the two sets of driving rolls, is also used to detect the difference in speed between the first and second sets of driving rolls.
Typically, the basic purpose of a dancer roll is to maintain constant the tension on the continuous web which traverses the span between the first and second sets of driving rolls, including traversing the dancer roll.
As the web traverses the span, passing over the dancer roll, the dancer roll moves up and down in a track, serving two functions related to stabilizing the tension in the web. First, the dancer roll provides a tensioning force to the web. Second, the dancer roll temporarily absorbs the difference in drive speeds between the first and second sets of driving rolls, until such time as the drive speeds can be appropriately coordinated.
A web extending between two drive rolls constitutes a web span. The first driving roll moves web mass into the span, and the second driving roll moves web mass out of the span. The quantity of web mass entering a span, per unit time, equals the web's cross-sectional area before it entered the span, times its velocity at the first driving roll. The quantity of web mass exiting a span, per unit time, equals the web's cross-sectional area in the span, times its velocity at the second driving roll. Mass conservation requires that over time, the web mass exiting the span must equal the mass entering the span. Web strain, which is proportional to tension, alters a web's cross-sectional area. Typically, the dancer roll is suspended on a support system, wherein a generally static force supplied by the support system supports the dancer roll against an opposing force applied by the tension in the web and the weight of the dancer roll. The web tensioning force, created by the dancer system, causes a particular level of strain which produces a particular cross-sectional area in the web. Therefore, the web mass flowing out of the span is established by the second driving roll's velocity and the web tensioning force because the web tensioning force establishes web strain which in turn establishes the web's cross-sectional area. If the mass of web exiting the span is different from the mass of web entering the span, the dancer roll moves to compensate the mass flow imbalance.
A dancer roll generally operates in the center of its range of travel. A position detector connected to the dancer roll recognizes any changes in dancer roll position, which signals a control system to either speed up or slow down the first driving roll to bring the dancer back to the center of its travel range and reestablish the mass flow balance.
When the dancer roll is stationary, the dancer support system force, the weight of the dancer roll, and the web tension forces are in static equilibrium, and the web tension forces are at their steady state values. Whenever the dancer moves, the web tension forces change from their steady state values. This change in web tension force supplies the effort that overcomes friction, viscous drag, and inertia, and causes the dancer motion. When the dancer moves very slowly, viscous drag and inertia forces are low and therefore the change in web tension is slight. However, during abrupt changes in mass flow, as during a machine speed ramp-up or ramp-down, the viscous drag, and inertia forces may be several times the web's steady state tension values.
The dancer roll's advantages are that it provides a web storage buffer that allows time to coordinate the speed of machine drives, and the dancer provides a relatively constant web tension force during steady state operation, or periods of gradual change. A limitation of dancer rolls, as conventionally used, is that under more dynamic circumstances, the dancer's ability to maintain constant web tension depends upon the dancer system's mass, drag, and friction.
It is known to provide an active drive to the dancer roll in order to improve performance over that of a static system, wherein the web is held under tension, but is not moving along the length of the web, whereby the dynamic,disturbances, and the natural resonance frequencies of the dancer roll and the web are not accounted for, and whereby the resulting oscillations of the dancer roll can become unstable. Kuribayashi et al, "An Active Dancer Roller System for Tension Control of Wire and Sheet." University of Osaka Prefecture, Osaka, Japan, 1984.
More information about tension disturbances and response times is set forth in U.S. Pat. No. 5,659,229 issued Aug. 19, 1997, which is hereby incorporated by reference in its entirety. U.S. Pat. No. 5,659,229, however, controls the velocity of the dancer roll and does not directly control the acceleration of the dancer roll.
Thus, it is not known to provide an active dancer roll in a dynamic system wherein dynamic variations in operating parameters are used to calculate variable active response force components for applying active and variable acceleration to the dancer roll, and wherein appropriate gain constants are used to affect response time without allowing the system to become unstable.